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Binary and Powers of 2
WARNING: INCOMING MATH The binary system in mathematics is a base-2 numeral system, as opposed to our usual base-10, or decimal, system. The decimal system uses ten digits, 0 through 9, before adding a second digit and returning to 0, thereby representing its base, ten, as 10. The binary system uses only two digits, 0 and 1, before doing likewise, thereby representing its base, two, also as 10. Counting in binary therefore runs as follows: Binary is the basis of conventional computing because a binary digit, or bit, can represent, or be represented by, anything that can be in one of two states, allowing computers to encode information using a series of "switches". 1 = on = true; 0 = off = false. Particularly important numbers in computing are powers of 2, represented above in bold, and numbers one less than a power of 2, represented in italics. A power of 2 is any number that can be gotten by multiplying 2 by itself a given number of times; n'' 2s multiplied together is 2 to the power of ''n, or 2^''n''. For any given number of bits b'', 2^''b different values can be represented, but since the lowest value is always 0 (with all the bits set to 0), the highest value is 2^''b'' − 1 (with all the bits set to 1). Thus, four bits can give 16 different values, ranging from 0 to 15; for the actual value 16, a fifth bit must be added. Uses in ReBoot * Binomes are walking, talking 0s and 1s. * Colorful ribbons of binary can be seen streaming around Mainframe, and random binary is frequently in evidence in places where text would be expected. * Ages are presented in binary (with a leading 0 if necessary to bring them up to two digits). * Pearson's Data Dump is located in Sector 1001 (9). * Al's Wait 'n' Eat is located on Level 31 (2^5 − 1). (It is also sometimes referred to as being in Sector 31; while this was probably an error, there is no reason it could not be at the intersection of the two.) * "Racing the Clock": ** "Well, it's not exactly new... if you call 31 nanoseconds new." (2^5 − 1) ** In the Game, all the binomes have cars numbered 00, Enzo has 01, Dot has 10, and Bob has 11 (0, 1, 2, 3). * "Quick and the Fed": ** The number Bob takes in Al's is 1000000000000, 4096 (2^12). ** The viral binomes in Al's have plates of little 1s and 0s. * "The TIFF": "...and you missed your flight to Sector 1101." (13) * "The Crimson Binome": "He's already downtimed 16 of our shipmates, Captain!" (2^4) * "Wizards, Warriors and a Word from Our Sponsor": "Mike! For the 128th time! Stop!" (2^7) * "Talent Night": ** Johnny O'Binome's joke runs as follows: 1010011011101110111001101111001110101100001100101110011101 This is simply Henny Youngman's famous one-liner "Take my wife... please!" translated into A1Z26 substitution cipher and from there into binary. (TAKE = 20 1 11 5 = 10100 1 1011 101, and so on.) It is not ASCII code, which, while apropos, would have been considerably longer. ** There is a countdown to Enzo's model upgrade which displays in binary while the crowd counts out loud "normally". * Identity Crisis: Part 1": ** Dot is attempting to free Sector 1000 (8). ** The graffiti Dot and Bob pass on the way to the secret meeting include "10110" (22) and a game of tic-tac-toe in 1s and 0s. * One Season 2 episode, we don't know which, is said to have city lights spelling out in binary code "Redacted you, broadcast standards." * At the party in "Mousetrap", in addition to the usual donuts, there are some vaguely rectangular cakes which serve as 1s to the donuts' 0s. * Daemon's virals count down in binary before self-destructing. The number they count down from has nothing to do with powers of 2, however. In "What's Love Got To Do With It?", Daecon counts down from 101 (5); in "Sacrifice", the masses count down from 111100 (60), despite the fact that ReBoot's whole time... situation means that minutes aren't even close to what they use at this scale, and even if they did, most of the numbers take well over a second each to say. (Of course, if they were counting down from, say, a microsecond in nanoseconds, they'd have to count from 1111101000, which would be impractical.) Non-Canon The ReBoot Style Guide for Season 1 declares Frisket's age to be "64 (in dog speed)" (2^6). This should be taken with a grain of salt, as all the ages that do specify a unit have them in hertz. Category:Computing concepts